On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case

Abstract : In [3], the authors proved that uniqueness holds among solutions whose exponentials are $L^p$ with $p$ bigger than a constant $\gamma$ ($p>\gamma$). In this paper, we consider the critical case: $p=\gamma$. We prove that the uniqueness holds among solutions whose exponentials are $L^\gamma$ under the additional assumption that the generator is strongly convex.
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Freddy Delbaen, Ying Hu, Adrien Richou. On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2015, 35 (11), pp.5273-5283. ⟨10.3934/dcds.2015.35.5273⟩. ⟨hal-00802330v2⟩

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